phukraut

I came upon an article on <a href="http://www.guardian.co.uk/life/science/story/0,12996,1320625,00.html">the greatest equations of all time</a>. I was inspired. So, along similar lines as the coolest number thread, what is your favourite formula (from math or science), equation, theorem, etc.?

Mine is the Binomial Theorem.



I always thought it was very elegant and simple, but powerful.

fckm

Schrodinger's Equation. Because no one understands where it comes from, and it tells us so damn much.

debianuser

The golden mean is my fav of all time

http://www.vashti.net/mceinc/golden.htm

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ice ice baby

1010011010

PV = nRT

Merely for the reason that I read it as "pervert".

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Simple Machines in Higher Dimensions

Paradise Lost

x^n + y^n = z^n where n is all integers > 1.

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"Marino could do it."

Rabid Bunny

Pythagorean Theorem.

a^2 + b^2 = c^2

Because I just love triangles. And it's the most used formula in my math classes.

gremlinx8

I don't know about my favorite, but I've found that F=ma and e=mc² have always been pretty helpful in school.

Mattbastard

The sine and cosine laws.

Those are very helpful for alot of engineering problems.

(theta) = tan^(-1) ((v^2)/(rg)) is a good one too for Centrifugal acc.

stingc

There are so many neat theorems, but I'd have to say Noether's is my favorite. It essentially states that any continuous symmetry has a conserved quantity associated to it. In newtonian mechanics, this shows that the conservation of energy is equivalent to saying that our label for time=0 is arbitrary. Similarly, momentum conservation comes from invariance under translations and angular momentum conservation is equivalent to rotational symmetry.

molloby

Well, I've always loved this one:



And this is just wonderfull, just for the fact that it actually works.



Schrodinger's Equation equation is great too. We do know where it comes from though, it is essentially a conservation of energy relationship. We're just not sure why it works.

namnori

Are you just using this to find a good answer to the Google Labs Aptitude Test (GLAT)?

phukraut

namnori, just in case that wasn't a joke: No!

FngKestrel

To be totally childish for a second, I'd have to say

6922251 x 8

would have to be one of my favorites.

Seriously though, I love the projectile motion equations. It's fun trying to convince students that X and Y are independent of each other.

Bossnass

(sigma)F=0

Few are as simple and as useful.

shred_head

I'd have to say Newton's Law of Gravitation and the oh so similar Coulomb' Law. They're both so useful and lead to so many different things.

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"Great spirits have always encountered violent opposition from mediocre minds" -- Albert Einstein

"A clear indication of women's superiority over man is their refusal to play air guitar." --Frank Zappa

CSflim

1+1=2

You can't beat the classics.

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MageB420666

Quadratic equation, cause it's the only formula that I can say off the top of my head without thinking for a second, I even have to think to remember the formula for the area of a rectangle.

-b(plus/minus) (the square root of(b^2 -4ac))/2a

Used to find the roots of a formula in the form of:

ax^2 + bx + c

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Apathy: The best outlook this side of I don't give a damn.

1slOwCD8

My favorite is the slope of a line y=mx+b. Or how about perimeter of a square 2(l+w)

Tophat665

The special case of the Euler equation has been my favorite since third year of college:

<i>e</i>^<i>i</i>&pi;=-1

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Set a man on fire, and he will be warm for the rest of his life.

shred_head

If it's a square wouldn't the perimeter just be 4*a, where "a" is the length of a side?

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"Great spirits have always encountered violent opposition from mediocre minds" -- Albert Einstein

"A clear indication of women's superiority over man is their refusal to play air guitar." --Frank Zappa

1slOwCD8

Yea, woops! Of course, if its a sqare all the sides would be even. I meant rectangle.

Thermopyle

the Maxwell equations. The look good and considering they're like 160 yeas old make's it an impressive discovery.

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- William Shatner.

Ydde

Integration of e^x = e^x .

It strike me because the integral of e^x gave you back the same e^x. I thought it was special.

And it reminded me of a joke in Tilted Humor, I think it's the geek joke thread.

Slavakion

e^x is also its own derivative. It boggles the mind.

Wait... some number raised to all integers greater than one, plus another number raised to the same, equals a third number raised to same. What would you use that for? And does that mean that x can be raised to any integer n, or is raised to all simultaneously?

filtherton

Baby, the limit as you and i approach the future is infinity.

mo42

6 x 7 = 42

Douglas Adams rules.

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It's not getting what you want, it's wanting what you've got.

CSflim

no!

6 x 9 = 42

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CSflim

x^n + y^n != z^n for all integers n > 2, for any integers x,y,z.

EDIT: I have a truly marvelous proof of this, but it won't fit into this text box.

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molloby

I think the fundamental theorem of calculus is quite amazing actually:

The integral of a function is the anti-derivative of that function. It is absolutely amazing that that works.

Thermopyle

It's fermats formula. There's no xyz integer solution for n>2. Get it right, or else you lose the hole point.

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Live life like you're gonna die, beacause you're gonna!

- William Shatner.

FngKestrel

Buahahahh...awesome.

Pragma

Yes, it is 6x9 = 42. And yes, as Douglas Adams himself said: "No one makes jokes in Base 13."

Personally, I like Gauss's Formula. Makes my summations easier.

Cryptic

mine's pretty obvious

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F=MA
2.998*108ms-1
Ek = 1/2mv2
R D R R

ratiocination

The Euclidean Algorithm and the properties of e !

flstf

The shortest distance between two points is a straight line in the opposite direction. Don't know the formula yet.

noodles

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radioguy

FOIL - first one i remember learning. for those that may have forgotten, although nobody probably has:

F - first
O - outer
I - inner
L - last

i'm definitely an algebra person, geometry sucked!

Ydde

OK, what does this formula do? I can't for the life of me remember this formula? Algebra manipulation?

phukraut

When you are multiplying two binomials:

(a + b)(c + d)

do First terms (ac); Outer terms (ad); Inner terms (bc); Last terms (bd). Gives

ac+ad+bc+bd.

Corneo

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Its so elegant, what with its partial derivatives...